Unfortunately there is little detail information in the mentioned section. According to the docs I created a Wix setup for a HelloWorld test add-in. In the wizard I set localization property to neutral and ticked English and German in the 3rd step.
This outputs a setup whith the following language files: StandardUI_de-DE.wxl, StandardUI_en-US.wxl and StandardUI_neutral.wxl.
But when I try to compile, I get the following error:

LGHT0309: Failed to open merge module for validation. The most common cause of this error is specifying that the merge module supports multiple languages (using the Package/@Languages attribute) but not including language-specific embedded transforms. To fix this error, make the merge module language-neutral, make it language-specific, embed language transforms as specified in the MSI SDK at http://msdn.microsoft.com/library/aa367799.aspx, or disable validation.

I did some more testing and it turns out it seems to be a sorting issue. The WixDesigner gives me the following order for the language id's in use

Languages="1033,1031,3072,0"

.
If I change that to

Languages="0,1031,1033,3072"

the compiler no longer complains and 3 msi files are created (Neutral, English, German).
The log looks quite promising as torch.exe and vdwtool.exe are called after msi creation.
I can see the transform files created under "obj\Release\Harvested MST".
Vdwtool.exe is picking them up, I assume vwdtool is responsible for the merge part.

Despite the fact that the build worked out, the "bin\Release\HelloWorldSetup.msi" does not respond to changed region settings. For testing I run the setup on a machine set up in German, but setup came up in English.
I checked whether or not the German transform has been merged correctly using msiexec.exe /i HelloWorldSetup.MSI TRANSFORMS=":1033" and voila setup comes up in German. This indicates the the merge was ok but there is an issue with language id's.

I ran the "handmade" MUI installer on the test machine set up in German and it came up in German.
I changed the region setting on that particular machine to United Kingdom, started the setup again and it came up in English.

Is it possible that vdwtool.exe is setting the language id's in the wrong order (follow up issue due to the above mentioned language id sorting I had to change in order to convince the compiler to do its job)?

This is not in line with what product.wxs shows (Languages="1033,1031,3072,0").
As mentioned above, if I change the sort order compilation works.

The machine I am using for development was once set up with CultureInfo.InstalledUICulture = "en-US".

I tested the MUI setup created by ADX on 2 machines.
The development machine with UICulture changed to "de-DE" and on another machine which was set up with CultureInfo.InstalledUICulture = "de-DE". In both cases setup started in English.

I also tested the "handmade" MUI setup on both machines. In both cases setup started in German.

The 'WiXDesignerProperties' group is used by the WiX Designer at the design time.
We can't reproduce the issue on our PCs. I will setup a VPC with culture de-DE and test your project again. I will let you know about results soon.

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